The program manager is typically an executive, so he is usually higher in the food chain than the functional manager (who is usually in middle management). Nevertheless, it is possible to have a program manager as a functional manager at the same time.
Now about the infinite authority over the resources, this depends on your organizational structure. If you're in project matrix structure, then yes, the Program Manager does have this supreme power of the resources. If you're in a functional organizational structure, then it is possible (but not necessary) for the program manager to still have the infinite authority over the resources, as in this type of structure, it is nearly a given that a program manager is also a high level executive. In either case, the authority is rarely, if ever, exercised.